Three Dead Outlet Mystery

One in the basement (washing machine)
Two on the first floor
The three outlets are dead, no power
All three worked fine up until now
So Far:
I have changed , tested all three outlets with a volt stick
None of them show any signs of having power
All circut breakers are on in the house
Everything else in the house works fine

It's probably a loose or broken connection. Many times, one circuit will feed multiple receptacles in a daisy chain. Break that chain somewhere, and those downstream stop working. So, looking at those receptacles, if you find one that only has one cable coming into it that doesn't work, it is the end of that chain...you have to work your way backwards and find those with two (or more) cables coming into the box, and see if there is power on one set, but none going out (probably because of either a loose connection, or a broken wire). There are tools that inject a signal into the wiring that you can trace, but baring purchasing one of those, you have to think logically on how the things were probably wired - most likely from one next to it, or directly above or below.

"backfeeding could be dangerous, because if the broken wire is the neutral, and you backfeed with the wrong polarity, you could cause a major short circuit. You have to remove outlets and visually inspect them to try to determine the power routing, in order to trace back to the point where you DO have power.

It's likely that the GFCI is the FIRST receptacle on that line, otherwise, it would not have something connected to the load side. Are you sure that it is not tripped? Have you tried the test button and pressed the reset? If the reset button won't stay in, you have a wiring problem down the line. It's also possible that the GFCI is bad, but more likely that there's a wiring problem, or the thing just tripped because of something you plugged into it was faulty.

Prior to the 3 receptacles losing power have you touched, moved, changed, installed or re-configured any electrical device(receptacle, switch, fan, light, etc..) anywhere in the house within say 72 hours of the 3 receptacles losing power. That would be a good place to start looking for a loose connection.

First, a washer/dryer should be on it's own circuit! If there's one cable coming in, how are all four of the wires connected to a GFCI? You CANNOT connect the line and load leads together. If there's nothing going out, only the LINE leads should be connected to something, and the load leads capped, assuming it has pigtails coming out, or if not, just leave the screws empty. The LOAD leads only get connected if you wish to protect and power additional 'normal' receptacles downstream of it.